Question

Which of the following steps would you perform to the system of equations

below so that the equations have opposite y-coefficients?
4x+2y = 4
12X - Y = 26
A. Divide both sides of the top equation by 3
•
B. Divide both sides of the bottom equation by 3
• C. Multiply both sides of the bottom equation by 2
• D. Multiply both sides of the top equation by 2

Answer 1

Answer: Choice C

Multiply both sides of the bottom equation by 2

Reason:

The y coefficient of the first equation is 2. For the other equation, that y coefficient is -1. We need these coefficients to be equal but opposite. One way to do this is to double everything in the bottom equation

The bottom equation 12x-y = 26 doubles to 24x - 2y = 52

At this point we have the equivalent system of

`\begin{cases}4x+2y = 4\\24x-2y = 52\end{cases}`

And we can see that we have equal but opposite y coefficients (2 and -2). The y terms add to 0 since 2y + (-2y) = 0y = 0 meaning we've eliminated y.